Question

Can someone please help me? MEDAL!


Evaluate the limit, if it exists.
\(\huge\frac{6n^2+4n}{n^2+5}\)

@ParthKohli @paki @confluxepic @Zale101 @EclipsedStar @AlexandervonHumboldt2 @iGreen @hartnn

Answer 1

As it tends to infinity?

Answer 2

I don't know...

Answer 3

That's all the question says...

Answer 4

Must be to infinity. In that case, divide both the numerator and denominator by n^2 and see how the thing would act as n approaches infinity

Answer 5

n96254

Answer 6

Actually, I'd prefer using L'Hopital's Rule.

Answer 7

So...
\(\huge \frac{n^2(6+\frac{4}{n})}{n^2(1 + \frac{5}{n^2})}\)

???

Answer 8

like that?

Answer 9

Which would simplify to
\(\huge \frac{6+\frac{4}{n}}{1+\frac{5}{n^2}}\)

Answer 10

Or maybe you could do it the pure way.\[\lim \dfrac{6n^2 + 4n}{n^2 + 5} = \lim \dfrac{6n^2 + 4n}{n^2} = \lim 6 + 4/n\]

Answer 11

And no, please ignore what I said earlier.

Answer 12

How did you get rid of the 5?

Answer 13

There is 5..

Answer 14

Actually, whatever, the other one works too.

Since the denominator is approaching infinity either way, no one cares about the + 5.

Answer 15

@StudyGurl14 just put n = infinity for what you have done..

Answer 16

So, I just say no limit? @ParthKohli ?

Answer 17

There is..

Answer 18

No.

As n approaches infinity, what happens to your fraction?

Answer 19

I am getting a finite value..

Answer 20

What happens to 4/n and 5/n^2 as n starts to grow bigger and bigger?

Answer 21

The nubers get smaller

Answer 22

Yeah, they get smaller. Ultimately, what number do they specifically reach (almost)?

Answer 23

0?

Answer 24

you end up with:
\[\large \frac{6 + \frac{4}{n}}{1 + \frac{5}{n^2}}\]

Answer 25

yes, you are right..

Answer 26

As you will put n = infinity, the fractions will become 0 and what are you left with now?

Answer 27

what do you mean "what are you left iwht now?"

Answer 28

See, I try to show you :P

Answer 29

\[\large \frac{6 + \frac{4}{n}}{1 + \frac{5}{n^2}} \implies \frac{6 + \frac{4}{\infty}}{1 + \frac{5}{\infty}} \implies \frac{6 + 0}{1 + 0}\]

Answer 30

Thank you @eta
:)